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lab2(CM) ver 1.0

allekco Nov 16th, 2019 87 Never
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  1. def f1(x, y, z):
  2.     return 9*x*z**2 + y*z + 2*y**2*x**3 + 175
  3.  
  4.  
  5. def f2(x, y, z):
  6.     return 0.5*y**3*z**2 - 0.8*x**2*y - 5.5 + 4.2
  7.  
  8.  
  9. def f3(x, y, z):
  10.     return 0.7*z**3 - 6.3*y**3 - 12.6
  11.  
  12.  
  13. def f1_der_x(x, y, z):     #derivative
  14.     return 9*z**2 + 6*y**2*x**2
  15.  
  16.  
  17. def f1_der_y(x, y, z):
  18.     return z + 4*y*x**3
  19.  
  20.  
  21. def f1_der_z(x, y, z):
  22.     return 18*x*z + y
  23.  
  24.  
  25. def f2_der_x(x, y, z):
  26.     return -1.6*x*y
  27.  
  28.  
  29. def f2_der_y(x, y, z):
  30.     return 1.5*y**2*z**2 - 0.8*x**2
  31.  
  32.  
  33. def f2_der_z(x, y, z):
  34.     return y**3*z
  35.  
  36.  
  37. def f3_der_x(x, y, z):
  38.     return 0
  39.  
  40.  
  41. def f3_der_y(x, y, z):
  42.     return -18.9*y**2
  43.  
  44.  
  45. def f3_der_z(x, y, z):
  46.     return 2.1*z**2
  47.  
  48.  
  49. def w_matrix(x, y, z):
  50.     W = [[f1_der_x(x, y, z), f1_der_y(x, y, z), f1_der_z(x, y, z)],
  51.          [f2_der_x(x, y, z), f2_der_y(x, y, z), f2_der_z(x, y, z)],
  52.          [f3_der_x(x, y, z), f3_der_y(x, y, z), f3_der_z(x, y, z)]]
  53.     return W
  54.  
  55.  
  56. def def_matrix(a=[]):
  57.     return (a[0][0]*a[1][1]*a[2][2] + a[2][0]*a[0][1]*a[1][2] +
  58.             a[1][0]*a[2][1]*a[0][2] - a[2][0]*a[1][1]*a[0][2] -
  59.             a[0][0]*a[2][1]*a[1][2] - a[1][0]*a[0][1]*a[2][2])
  60.  
  61.  
  62. def t_matrix(a=[]):
  63.     a1 = a[0][0]
  64.     a2 = a[1][0]
  65.     a3 = a[2][0]
  66.     b1 = a[0][1]
  67.     b2 = a[1][1]
  68.     b3 = a[2][1]
  69.     c1 = a[0][2]
  70.     c2 = a[1][2]
  71.     c3 = a[2][2]
  72.     B = [[a1*b2-a2*b1, -a2*c3+a3*c2, a2*b3-a3*b2],
  73.          [-b1*c3+b3*c1, a1*c3-a3*c1, -a1*b3+a3*b1],
  74.          [b1*c2-b2*c1, -a1*c2+a2*c1, a1*b2-a2*b1]]
  75.     return B
  76.  
  77.  
  78. def inverse_matrix(a=[]):
  79.     T = t_matrix(a)
  80.     q = def_matrix(a)
  81.     if def_matrix(a) == 0:
  82.         print("def_matrix = 0")
  83.         return a
  84.     for i in range(3):
  85.         for k in range(3):
  86.             a[i][k] = T[i][k]/q
  87.     return a
  88.  
  89.  
  90. def output_matrix(a=[]):
  91.     print(a[0][0], ' ', a[0][1], ' ', a[0][2])
  92.     print(a[1][0], ' ', a[1][1], ' ', a[1][2])
  93.     print(a[2][0], ' ', a[2][1], ' ', a[2][2])
  94.     print('')
  95.  
  96.  
  97. x = -2.8 #начальное решение
  98. y = -0.2
  99. z = 2.6
  100. print(f1(x, y, z))
  101. print(f2(x, y, z))
  102. print(f3(x, y, z))
  103. print('')
  104.  #[номер строки][номер столбца]
  105. #W = [[2,1,1],[1,2,1],[1,1,2]]
  106.  
  107. for i in range(10):
  108.     W = w_matrix(x, y, z)
  109.     I = inverse_matrix(W)
  110.     x2 = x - (I[0][0]*f1(x,y,z) + I[0][1]*f2(x,y,z) + I[0][2]*f3(x,y,z))
  111.     y2 = y - (I[1][0]*f1(x,y,z) + I[1][1]*f2(x,y,z) + I[1][2]*f3(x,y,z))
  112.     z2 = z - (I[2][0]*f1(x,y,z) + I[2][1]*f2(x,y,z) + I[2][2]*f3(x,y,z))
  113.  
  114.     x=x2
  115.     y=y2
  116.     z=z2
  117.     print(f1(x, y, z))
  118.     print(f2(x, y, z))
  119.     print(f3(x, y, z))
  120.     print('ответ: ', x, y, z)
  121.     print('')
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